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Stochastic Unit Commitment
Abstract ~~ Write the first paragraph of your page here. Introduction Unit Commitment (UC) is an optimization problem that generates commitment status and generation dispatch of various generating units in a way that minimizes the operating cost, including several operating constraints such as generator minimum / maximum generation limits, ramping limits, minimum up/down time constraints, time-dependent start-up costs, and transmission capacity limits. The system operator makes commitment and dispatch decisions over generation units in order to satisfy the demand and reliability requirements. The system operator should take several factors into account that cause uncertainties such as load forecast error, changes of system interchange schedule, and unexpected transmission and generation outages. Deterministic Unit Commitment vs Stochastic Unit Commitment There are two approaches in solving the unit commitment problem that differ in addressing the uncertainty. Deterministic unit commitment formulation is a traditional solution where the load is modeled with one forecast, while the next day situation including uncertainties is assumed to be fixed, and handled by imposing deterministic reserve requirements. On the other hand, stochastic approaches consider uncertainties for the situations in the scheduling time interval. There are two types of modeling and solution approaches for stochastic unit commitment which are distinct in handling the uncertainties. Robust unit commitment (RUC) models manage uncertainty based only on the information of the range of the uncertainty without any information of probability distributions. RUC produces conservative solutions by optimizing the cost of the worst case among all the scenarios generated from the uncertainties. Stochastic unit commitment(SUC) models probabilistic scenario based on uncertainty representation, in which a large number of scenarios are generated with probability weighted on each cases according to the information of probability distributions. Due to increasing penetration of renewable energy resources, addressing uncertainties rigorously is getting more important, which leads to imposing larger amount of reserve requirement, thus resulting in higher operation cost in deterministic unit commitment. Stochastic programing is advantageous because it can minimize total expected operation cost while satisfying the reliability improvement. P. Ruiz, C. Philbrick E. Zak, K.Cheung, and P. SauerP. Ruiz, C. Philbrick, E. Zak, K. Cheung, and P. Sauer, “Uncertainty management in the unit commitment problem,” IEEE Trans. Power Syst., vol. 24, no. 2, pp. 642–651, May 2009. P. Ruiz, C. Philbrick, and P. Sauer, “Modeling approaches for computational cost reduction in stochastic unit commitment formulations,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 588–589, 2010. This paper focuses on two-stage models and algorithms associated with stochastic unit commitment and the various methods that can help find the optimal solution for this type of problems. The struture of Stohastic Unit Commitment Stochastic UC is formulated as a two-stage problem that determines the generation schedule that minimizes the expected cost over all of the scenarios respecting their probabilities. In a two-stage SUC model, two parts of modeling can be discussed. The first part is modeling uncertainties by generating scenarios and the second part is modeling decisions in unit commitment problem. It is quite computationally demanding to include a large number of generated scenarios while solving the problem. Therefore, scenarios with ignorable probabilities can be reduced by scenario reduction methods. Similar scenarios in their probability, hourly magnitude, or the resulting cost can be aggregated so that the computational burden is significantly decreased. UC decision part is divided into two parts : day-ahead decisions (first stage) and real-time decisions (second stage). The day-ahead decisions are unique over all the scenarios, while real-time decisions are scenario-dependent. This means that UC solution is the solution that can manage all the possible scenarios. In the first stage, the model makes commitment decisions for all units, especially traditional units. Q. P. Zheng, J. Wang, P. M. Pardalos, and Y. Guan, “A decomposition approach to the two-stage stochastic unit commitment problem,” Ann. Oper. Res., vol. 210, no. 4, pp. 387–410, 2013. Several factors that should be determined ahead of scheduling time are included for optimization, such as start-up/shut-down cost of conventional generators and contract cost of demand-side resources. In the second stage, factors that should be considered for real-time operation are included for optimization, such as generation cost where dispatches and reserves of multiple periods are included, deployment cost of demand-side reserve, and cost related to the involuntary load shedding. Hyungon Park, "Stochastic Security-Constrained Generation Scheduling with Wind Power Generation based on Dynamic Line Rating", 2016. Solution Algorithm for Stochastic Unit Commmitment(SUC) Since SUC includes large number of scenarios, stochastic unit commitment problem is a large-scale mixed-integer non-linear program. Benders Decomposition ABCD Lagrangian Relaxation EFGH ---